Question

Which statement explains why correlation could be 0 even if a strong relationship between two variables existed?

Group of answer choices

Since the correlation is 0, there is no strong relationship between the two variables; and a scatterplot would be misleading.

Correlation can be 0 even if there is a strong linear relationship between the variables.

Correlation only measures the strength of the relationship between two variables when the units of the two variables are the same.

Correlation does not describe curved (nonlinear) relationships between variables.

Answer #1

Sol:

since correlation=0

there is no linear relationship between two variables

However,this is only for linear relationship.It is possible that variables have a strong curvilinear relationship

If a strong linear relationship between two variables existed then correlation coefficient=1

If a strong curvilinear relationship between two variables existed then correlation coefficient can be zero

**Correlation does not describe curved (nonlinear)
relationships between variables**.

Correlation is a visual method for determining the relationship
between two variables... including linear, curve linear, strong,
weak, positive, negative, and no relationships. The correlation
coefficient is a mathematical reflection of that relationship.
Regression analysis is the same thing as the correlation
coefficient. True or False

Why is it advisable to generate a scatterplot before computing a
correlation coefficient between two variables? Describe how a
scatterplot might differ when viewing correlations that represent
positive, negative, and no relationship between predictor and
criterion variables. Is it possible to have a relation between
variables that systematic (i.e., reliable and predictable) yet not
linear?

A) Two variables have a high covariance. This means the two
variables have a strong relationship. T/F
B) For a variable x, the sample mean is 8 and the sample
standard deviation is 2. One of the observations is 15. Is this
observation an outlier?
Group of answer choices
Yes, the z-score is greater than 3
No, the z-score is between -3 and 3
Yes, the z-score is between -3 and 3
No, the z-score is less than -3
C)...

1. Name two ways in which two variables could be related. Select
the two most correct answers. Choose the correct answer below.
A) Strong and moderate B) Moderate and negative C) Weak and
moderate D) strong and weak
2. Name a graph that can be used to quickly illustrate the
relationship between two variables? Choose the correct answer
below.
A) Histogram B) Regression line C) Scatter plot D) Time series
graph.
3. What do we mean by the strength of...

correlation measures the degree to which two variables are
related to one another.
Here are the definitions of the three possibilities:
Positive correlations: In this type of
correlation, both variables increase or decrease at the same time.
A correlation coefficient close to +1.00 indicates a strong
positive correlation.
Negative correlations: This type of
correlation indicates that as the amount of one variable increases,
the other decreases (and vice versa). A correlation coefficient
close to -1.00 indicates a strong negative correlation....

Describe the relationship between two variables when the
correlation coefficient r is near 0.

The covariance and correlation coefficient are measures that
quantify the non-linear relationship between two variables.
T/F

If
the correlation between two variables is close to 0, you can
conclude that a scatterplot would show
(a) a strong straight-line pattern.
(b) a cloud of points with no visible pattern.
(c) no strainght-line pattern but there might be a strong
pattern of another form.

Think about a group of people for a moment, then describe a
correlation, (between two variables of your choice) among them. Is
the correlation strong? What would you guess to be the r-value, the
linear correlation coefficient?

If you find a Pearson's correlation of zero between two
continuous variables, this means:
A. There is no relationship between the two variables
B. There is a strong relationship between the two variables
C. There may be a non-linear relationship between the two
variables
D. Two of these answers are correct

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